Question: Solve for $x$ and $y$ using substitution. ${-3x+4y = 10}$ ${y = 4x+9}$
Since $y$ has already been solved for, substitute $4x+9$ for $y$ in the first equation. ${-3x + 4}{(4x+9)}{= 10}$ Simplify and solve for $x$ $-3x+16x + 36 = 10$ $13x+36 = 10$ $13x+36{-36} = 10{-36}$ $13x = -26$ $\dfrac{13x}{{13}} = \dfrac{-26}{{13}}$ ${x = -2}$ Now that you know ${x = -2}$ , plug it back into $\thinspace {y = 4x+9}\thinspace$ to find $y$ ${y = 4}{(-2)}{ + 9}$ $y = -8 + 9$ $y = 1$ You can also plug ${x = -2}$ into $\thinspace {-3x+4y = 10}\thinspace$ and get the same answer for $y$ : ${-3}{(-2)}{ + 4y = 10}$ ${y = 1}$